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3 years ago

Pls help me find the volume of this solid

Mathematics

1 answer:

SVEN [57.7K]3 years ago

8 0

Answer:

240cm³

Step-by-step explanation:

First, let's assume the entire shape is full rectangular prism without that has the middle being cut out.

What this means is that, to get the volume of the solid made out of clay, we would calculate the solid as a full rectangular prism, then find the volume of the assumed middle cut-out portion. Then find the difference between both.

Let's solve:

Find the volume of the rectangular prism assuming the solid is full:

Volume of prism = width (w) × height (h) × length (l)

w = 4cm

h = 7cm

l = 3+6+3 = 12cm

Volume of full solid = 4*7*12 = 336cm³

Next, find the volume of the assumed cut-out portion using same formula for volume of rectangular prism:

w = 4cm

h = 7-3 = 4cm

l = 6cm

Volume of assumed cut-out portion = 4*4*6 = 96cm³

Volume of solid made from clay = 336cm³ - 96cm³ = 240cm³

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Given tan of theta = -2 and pi/2; find cos(2theta)

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Given tan of theta = -2 and pi/2; find cos(2theta)
The identity of cos (2 theta)= $cos(2\theta )=\frac{1-tan^2\theta }{1+tan^2\theta }$
Given tan of theta = -2 and pi/2.
So, let's plug in tan theta= -2
$cos(2\theta)= \frac{1-(-2)^2}{1+(-2)^2}$
= $\frac{1-4}{1+4}$ (Squaring)
= $\frac{-3}{5}$ (simplifying)
So, cos ( 2 theta) = -3/5.
Now we can plug in tan theta = π/2
$cos(2\theta)= \frac{1-(π/2)^2}{1+(π/2)^2}$
= $\frac{1-pi^2/4}{1+pi^2/4}$ (Squaring)
= $\frac{4-pi^2}{4+pi^2}$ Simplifying
So, cos ( 2 theta)= -3/5 and (4-pi^2)/(4+pi^2)

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4 years ago

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3 years ago

If 10000 is invested at an interest rate of 10 per year ,compound semiannually,find the value of the investment after the given

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Answer:

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Part b) $\$32,251.00$

Part c) $\$57,918.16$

Step-by-step explanation:

<u><em>The complete question is</em></u>

If $10,000 is invested at an interest rate of 10% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

a)6 years

b)12 years

c)18 years

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The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$